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Proving Relationships of Parallel and Perpendicular Lines

Proving Relationships of Parallel and Perpendicular Lines 1.4 - Solution

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To tell if two lines are perpendicular, we check if their slopes are negative reciprocals. For this exercise, we have been given two points on each line, so we have enough information to calculate their slopes using the Slope Formula. Note that when choosing points to substitute for and it doesn't matter which points on the line you choose, since the result will be the same. Let's start with line which passes through and
Simplify right-hand side
The slope of line is We will use the same method to identify the slope of line
Line Points Slope Simplified Slope

To determine whether or not the lines are perpendicular, we calculate the product of their slopes. Any two slopes whose product equals are negative reciprocals, and therefore the lines are perpendicular. We have found that lines and are perpendicular to one another.